On a class of nonlocal problems with fractional gradient constraint

  • Assis Azevedo

    Universidade do Minho, Braga, Portugal
  • José-Francisco Rodrigues

    Universidade de Lisboa, Portugal
  • Lisa Santos

    Universidade do Minho, Braga, Portugal
On a class of nonlocal problems with fractional gradient constraint cover
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Abstract

We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type Dσug|D^\sigma u|\leq g, involving the distributional fractional Riesz gradient DσD^\sigma, 0<σ<10<\sigma<1, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems.

We also prove their convergence as σ1\sigma\nearrow1 towards their local counterparts with the gradient constraint Dug|D u|\leq g.